

A004014


Norms of vectors in the b.c.c. lattice.
(Formerly M2347)


4



0, 3, 4, 8, 11, 12, 16, 19, 20, 24, 27, 32, 35, 36, 40, 43, 44, 48, 51, 52, 56, 59, 64, 67, 68, 72, 75, 76, 80, 83, 84, 88, 91, 96, 99, 100, 104, 107, 108, 115, 116, 120, 123, 128, 131, 132, 136, 139, 140, 144, 147, 148, 152, 155, 160, 163, 164, 168
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OFFSET

0,2


COMMENTS

These are numbers of the form x^2+y^2+z^2 where x, y and z are either all even (including zero) or all odd.
The selection rule for the planes with Miller indices (hkl) to undergo Xray diffraction in an f.c.c. lattice is h^2+k^2+l^2 = N where N is a term of this sequence. See A000378 for simple cubic lattice. (End)


REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", SpringerVerlag, p. 116. (Chapter 4 section 6.7)
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



MAPLE

f:= JacobiTheta2(0, z^4)^3+JacobiTheta3(0, z^4)^3:
S:= series(f, z, 1001):
select(t > coeff(S, z, t) <> 0, [$0..1000]); # Robert Israel, Oct 18 2015


MATHEMATICA

f = EllipticTheta[2, 0, z^4]^3 + EllipticTheta[3, 0, z^4]^3; S = f + O[z]^200; Flatten[Position[CoefficientList[S, z], _?Positive]  1] (* JeanFrançois Alcover, Oct 23 2016, after Robert Israel *)


CROSSREFS



KEYWORD

nonn,nice,easy


AUTHOR



EXTENSIONS



STATUS

approved



